57 3.7 ConclusionsThe study performed in this chapter showed the following: 1) Constraining the lateral sides of the slab at tie bars locations does not have any effect on slab response along the wheel-path, therefore, unconstrained boundaries are selected to be applied at the slab lateral sides. 2) Results from the FEM shows that, applying an unbonded interface at the slab/base course interface significantly reduces the tensile stresses and strains developed at the slab bottom along the transverse joint. Because most of rigid pavement distresses are mainly due to joint problems, applying an unbonded interface with friction at the slab/base interface may reduce the extent of stresses and strains induced at the joint and accordingly can diminish rigid pavement distresses caused by joint problems. 3) The FEM results obtained along the wheel-path shows that a transverse joint where the load is transferred by both dowel bars and aggregate interlock eliminates the sharp MPS reversals observed at slab top along the joint. It also reduces the tensile MPS induced at slab bottom. In addition, the same joint layout reduces the separation developed at the slab/base interface and therefore reduces the potential of pumping or loss of support, which may occur due to entrapped water. For these reasons the doweled joint without opening was selected for the study. 4) Using a symmetry plane boundary condition along the traffic direction has a minor effect on the structural response of the rigid pavement and results in great savings in model size, computer memory, and CPU time. Hence, symmetry plane boundary conditions are applied and only one half of a traffic lane is modeled. 5) The comparison between several FE models with different mesh refinement shows that the change in FE mesh size within the studied meshes did not affect the accuracy of the results obtained from FE modeling.
58 4x18 in.9 x 18 in.4x18 in.90 in.180 in.90 in.Symm etry Plan90 in.180 in.90 in.180 in.90 in.Symm etry Plan Lateral Sides Constrained at Tie BarsUnconstrained Lateral Sides(a) Finite Element Model with Lateral Sides Constrained at Tie Bars Locations(b) Finite Element Model with Unconstrained Lateral SidesFIGURE 3.1 Plane View of the Two Models Developed for Investigating the Effect of Tie Bars
59 FIGURE 3.2 Effect of Tie Bars on Distribution of Maximum Principal Stress in the Concrete Slab -150 -100 -50 0 50 100 150 200 -100 -50 0 50 100 Maximum Principal Stress (MPS), psi Distance from Element MT or MB, (in.) -150 -100 -50 0 50 100 150 200 -100 -50 0 50 100 Maximum Principal Stress (MPS), psi Distance from Element MT or MB, (in.) -200 -150 -100 -50 0 50 100 -40 -20 20 40 60 80 Maximum Principal Stress (MPS), psi Distance from Element JT or JB, (in.) -200 -150 -100 -50 0 50 100 -40 -20 20 40 60 80 Maximum Principal Stress (MPS), psi Distance from Element JT or JB, (in.) (a) (b) (c) (d) Symmetry Plane Bottom Top Symmetry Plane Bottom Top Symmetry Plane Symmetry Plane Bottom Top Bottom Top Sides Constrained at Tie Bars Unconstrained Sides Unconstrained Sides Sides Constrained at Tie Bars 0 0 X Y X Y X Y X Y
60 FIGURE 3.3 Effect of Tie Bars on Distribution of Longitudinal Strain in the Concrete Slab -150 -100 -50 0 50 100 150 200 -4 -3 -2 -1 0 1 2 3 4 x 10 -5 Longitudinal Strain (γx) Distance from Element MT or MB, (in.) -150 -100 -50 0 50 100 150 200 -4 -3 -2 -1 0 1 2 3 4 x 10 -5 Longitudinal Strain (γx) Distance from Element MT or MB, (in.) -200 -150 -100 -50 0 50 100 -2 -1 1 2 3 x 10 -5 Longitudinal Strain (γx) Distance from Element JT or JB, (in.) -200 -150 -100 -50 0 50 100 -2 -1 1 2 3 x 10 -5 Longitudinal Strain (γx) Distance from Element JT or JB, (in.) (c) (d) (a) (b) Symmetry Plane Bottom Top Symmetry Plane Bottom Top Symmetry Plane Symmetry Plane Bottom Top Bottom Top Sides Constrained at Tie Bars Unconstrained Sides Unconstrained Sides Sides Constrained at Tie Bars 0 0 X Y X Y X Y X Y
61 FIGURE 3.4 Effect of Tie Bars on Distribution of Transverse Strain in the Concrete Slab -150 -100 -50 0 50 100 150 200 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 x 10 -5 Transverse Strain (γy) Distance from Element MT or MB, (in.) -150 -100 -50 0 50 100 150 200 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 x 10 -5 Transverse Strain (γy) Distance from Element MT or MB, (in.) -200 -150 -100 -50 0 50 100 -3 -2 -1 1 2 3 x 10 -5 Transverse Strain (γy) Distance from Element JT or JB, (in.) -200 -150 -100 -50 0 50 100 -3 -2 -1 1 2 3 x 10 -5 Transverse Strain (γy) Distance from Element JT or JB, (in.) (a) (b) (c) (d) Symmetry Plane Bottom Top Symmetry Plane Bottom Top Symmetry Plane Symmetry Plane Bottom Top Bottom Top Sides Constrained at Tie Bars Unconstrained Sides Unconstrained Sides Sides Constrained at Tie Bars 0 0 X Y X Y X Y X Y
62 FIGURE 3.5 Effect of Tie Bars on Distribution of Vertical Strain in the Concrete Slab -150 -100 -50 0 50 100 150 200 -6 -5 -4 -3 -2 -1 0 1 2 x 10 -5 Vertical Strain Distance from Element MT or MB, (in.) -150 -100 -50 0 50 100 150 200 -6 -5 -4 -3 -2 -1 0 1 2 x 10 -5 Vertical Strain Distance from Element MT or MB, (in.) -200 -150 -100 -50 0 50 100 -16 -14 -12 -10 -8 -6 -4 -2 1 x 10 -5 Vertical Strain Distance from Element JT or JB, (in.) -200 -150 -100 -50 0 50 100 -16 -14 -12 -10 -8 -6 -4 -2 1 x 10 -5 Vertical Strain Distance from Element JT or JB, (in.) (a) (b) (c) (d) Symmetry Plane Bottom Top Symmetry Plane Bottom Top Symmetry Plane Symmetry Plane Bottom Top Bottom Top Sides Constrained at Tie Bars Unconstrained Sides Unconstrained Sides Sides Constrained at Tie Bars 0 0 X Y X Y X Y X Y
63 FIGURE 3.6 Effect of Concrete-Base Bond on Distribution of Maximum Principal Stress in the Concrete Slab -150 -100 -50 0 50 100 150 200 -100 -50 0 50 100 Maximum Principal Stress (MPS), psi Distance from Element MT or MB, (in.) -150 -100 -50 0 50 100 150 200 -100 -50 0 50 100 Maximum Principal Stress (MPS), psi Distance from Element MT or MB, (in.) -200 -150 -100 -50 0 50 100 -50 50 100 Maximum Principal Stress (MPS), psi Distance from Element JT or JB, (in.) -200 -150 -100 -50 0 50 100 -50 50 100 Maximum Principal Stress (MPS), psi Distance from Element JT or JB, (in.) (a) (b) (c) (d) Symmetry Plane Bottom Top Symmetry Plane Bottom Top Symmetry Plane Symmetry Plane Bottom Top Bottom Top 0 0 Bonded Interface (Tied) Bonded Interface (Tied) Unbonded Interface (Sliding with Voids) Unbonded Interface (Sliding with Voids) X Y X Y X Y X Y
64 FIGURE 3.7 Effect of Concrete-Base Bond on Distribution of Longitudinal Strain in the Concrete Slab -150 -100 -50 0 50 100 150 200 -4 -3 -2 -1 0 1 2 3 4 x 10 -5 Longitudinal Strain (εx)Distance from Element MT or MB, (in.) -150 -100 -50 0 50 100 150 200 -4 -3 -2 -1 0 1 2 3 4 x 10 -5 Longitudinal Strain (εx)Distance from Element MT or MB, (in.) -200 -150 -100 -50 0 50 100 -2 -1 1 2 3 4 x 10 -5 Longitudinal Strain (εx)Distance from Element JT or JB, (in.) -200 -150 -100 -50 0 50 100 -2 -1 1 2 3 4 x 10 -5 Longitudinal Strain (εx)Distance from Element JT or JB, (in.) (a) (b) (c) (d) Symmetry Plane Bottom Top Symmetry Plane Bottom Top Symmetry Plane Symmetry Plane Bottom Top Bottom Top Bonded Interface (Tied) Bonded Interface (Tied) Unbonded Interface (Sliding with Voids) Unbonded Interface (Sliding with Voids) 00 X Y X Y X Y X Y
65 FIGURE 3.8 Effect of Joint Opening on Distribution of Maximum Principal Stress in the Concrete Slab -150 -100 -50 0 50 100 150 200 -100 -50 0 50 100 Maximum Principal Stress(MPS), psi Distance from Element MT or MB, (in.) -150 -100 -50 0 50 100 150 200 -100 -50 0 50 100 Maximum Principal Stress(MPS), psi Distance from Element MT or MB, (in.) (a) (b) Symmetry Plane Symmetry Plane X Y X Y -200 -150 -100 -50 0 50 100 -40 -20 20 40 60 80 100 Maximum Principal Stress(MPS), psi Distance from Element JT or JB, (in.) -200 -150 -100 -50 0 50 100 -40 -20 20 40 60 80 100 Maximum Principal Stress(MPS), psi Distance from Element JT or JB, (in.) (c) (d) Symmetry Plane X Y 0 Bottom Top Bottom Top 0 X Y Symmetry Plane Bottom Top Bottom Top Without Joint Opening With Joint Opening With Joint Opening Without Joint Opening
66 FIGURE 3.9 Effect of Joint Opening on Distribution of Longitudinal Strain in the Concrete Slab -200 -150 -100 -50 0 50 100 -6 -4 -2 2 4 x 10 -5 Longitudinal Strain (γx) Distance from Element JT or JB, (in.) -200 -150 -100 -50 0 50 100 -6 -4 -2 2 4 x 10 -5 Longitudinal Strain (γx) Distance from Element JT or JB, (in.) (c) (d) Symmetry Plane X Y Symmetry Plane X Y 0 Bottom Top Bottom Top -5 -5 (b) -150 -100 -50 0 50 100 150 200 -4 -3 -2 -1 0 1 2 3 4 x 10 Longitudinal Strain (γx) Distance from Element MT or MB, (in.) -150 -100 -50 0 50 100 150 200 -4 -3 -2 -1 0 1 2 3 4 x 10 Longitudinal Strain (γx) Distance from Element MT or MB, (in.) (a) Symmetry Plane Symmetry Plane Bottom Top Bottom Top X Y X Y 0 Without Joint Opening With Joint Opening With Joint Opening Without Joint Opening